# Thread: Extended GCD algorithm for polynomials: write number 1/(a3+2a2+4), where a satisfies:

1. ## Extended GCD algorithm for polynomials: write number 1/(a3+2a2+4), where a satisfies:

Hi,
I am trying to solve a problem which asks to write number 1/(a3+2a2+4), where a satisfies: a4+2a3+2a2+8a = -2 without using other than rational numbers in the denominator. I came as far as reducing the problem to finding inverse of (x4+2x3+2x2+2s+2 + (f)) \in Q[x]/(f) (f) is here ideal generated by <a3+2a2+4>. Now I suppose I have to apply Extended Euclidean Algorithm for gcd(x4+2x3+2x2+2s+2, a3+2a2+4). However, I found out don't really know how to do the algorithm as I cannot get to Bezout's coefficients that are of degree <=3.
I attach a photo of my progress. I would like somebody to point out where I fail in executing the algorithm correctly as I cannot find out.
Thank you.